Betz' Law - The Maximum Efficiency of Wind Turbines

[@kev7355]

Amazing. Understood this in 10 minutes what took hours to explain in class.

[@treborg777]

I really like this derivation. Thanks for doing this and posting it. Too many others I've seen leave out the "m-dot" factor and just show an expression in which power is equal to kinetic energy, which is nonsense.

[@j121212100]

If that is the maxium power that can be extracted from an ideal turbine then i wonder what the maxium work a turbine can impart on the moving air. Glad you posted your presentation on youtube!

[@geejaysheehan3263]

At 7:22 you say that you make the assumption that Ut=Uu but then you say equation 3 is Ut=1/2(Ud+Uu). How can you use two different assumptions/equations for Ut at two different parts of this derivation?

[@2superlinkbros]

Naman is correct: it is only used for the "power in" calculation. But it can't be exactly true, or else power out would be exactly 0.

[@victorm.jimenez7134]

Yeah I think the correct assumption is that the velocity at which the mass flows through At in the intlet is Uu. Thus m_dot = (rho)(At)(Uu)

[@grahamflowers]

Has mr Betz forgoten about the fact that any object that stands in the wind is not just pushed but is also sucked by the air around it that can add to the force of the rotation of the blades or did mr Betz do his experyments in a closed space and not in the open or just did the maths

[@kingz.a1918]

Heads Mess jj

[@geejaysheehan3263]

I know you did not invent the Betz limit derivation but I was curious if you found why different assumptions are made for different parts of the derivation because that does not seem logical to me

[@vincentrobinette1507]

So, the fraction of 16/27 is an exact fraction, that only turns "irrational" when converted to decimal? This explanation suggests, that the fraction is not "rounded", but rather the exact percentage available from a "perfect turbine". If a turbine advertises "80% efficient, that means, 80% of ~59.25925%, for an overall efficiency of ~47.4074%.

[@2superlinkbros]

Interestingly, if U_t = U_u were true, then the equation 1/2(U_u + U_d)=U_t (or the arithmetic average equation) would imply that all velocities were equal. If that were true, then the turbine would not output any mechanical energy, as the pressures on both sides, P1 and P2, would also have to be equal (this comes from her equation 2). So that can't be exactly true. There's something going on here... Maybe it's only approximately true, and we are taking the limit as U_u approaches U_t, where the closer you get to this limit, the lower the power output, but the closer our efficiency gets to max efficiency. Kind of like a Carnot Heat engine.

[@grahamflowers]

the wind pushes on what it touches it can't push on the gaps between the blades regards Graham Flowers

[@IvernLumeria]

Very clear content. Thank you.

[@astherphoenix9648]

i like your voice derek

[@j121212100]

excellent derivation!

How to find Ud wind speed please

[@srinivasarao3546]

Thank you, derivation is good, except for one point. In the derivation, you have assumed Ut=Uu, it is not clear, because, we have already derived Ut=½(Uu+Ud). Some justification will be better.

[@de0509]

Also curious if it is right for me to imagine during the bernoulli eqn part that the Z will cancel out anyway if all the slices are taken into account? Because theres also a part below the nacelle where some of the gas goes downwards. Or is there something I have not thought of yet?

[@andikafadhila]

thanks for helping with my thesis! :'D

[@Kobs.A]

I plan to use this for my thesis as well

[@grahamflowers]

Betz limit has been smashed by the Gyro wind turbine regards Graham Flowers

[@ariskurt21]

The moment my family and I were sent our last electricity bill we could not place food on the kitchen table. I knew my kids would probably go hungry. We got into bank debt. The answer ended up being the Papziati Energy online guide. It is a great way to develop your own energy source. Google it.

[@Rayzoon]

My lecture slides in 10 mins.

[@shuvochowdhury1115]

Just wow!!

[@sasasasasa2360]

Зачем разбираться в законе Бетза, если есть 3 бочки - надо резать и варить. А вдруг и инвертер с акумулятором наидут?

[@bananian]

We should be converting kinetic energy to potential energy instead of simply transferring a part of the kinetic energy.

[@tempura_slayer]

Thank you!

[@حيدركاظم-ن7س2ه]

a power plant 800mw burns natural gas to boil water producing saturated steam 100% quality at 70 bar this steam is expanded in a turbine to steam at 100c and 1 bar the steam inters the turbine at 10 m/s and exits 5m below the entrance point level at 100m/s the turbine is connected to an electrical generator by ashaft the efficincy of the turbine is 60%.what is the mass flow rate of steam to the turbine?

[@davidwilkie9551]

Yes

[@orkhanj]

👍🏻👍🏻

[@AakarshSahay]

pog

[@phyarth8082]

Disk actuator where turbine blade geometry angle have no impacts or efficiency that is non-sense science. Reason why we have no effective reliable renewable energy based on turbine technology is reason of non-sense math where turbine is abstract disk, without blades angle of blade with wind have no impacts on efficiency. And in 100 year nanobody tried to improve or correct his mistake :(

[@grahamflowers]

Betz law has been smashed and debunked regards Graham

[@asadawan8649]

Any one can help me, for below mentioned questions? i need answer please Q 1-What is the present value of the payment cost made to decommission the wind farm (in € and answer as an absolute value)? Q 2-What is the present value of all the costs (in € and answer as an absolute value)? Q 3 -What is the levellised annual cost (in €/year and answer as an absolute value)? Q 4-What is the levellised cost of energy (LCoE) in €c/kWh and answer as an absolute value?

[@حيدركاظم-ن7س2ه]

solve this equstion for me please drctor please please please i need it